A394650 Number of index 12*n free subgroups of SL_2(Z).

20, 480, 17680, 867840, 53008000, 3868262400, 328200070400, 31743511756800, 3447768313600000, 415545796853760000, 55041558756762624000, 7948018349009534976000, 1242718216339451289600000, 209174003345404408627200000, 37712045770845433775923200000, 7250740898779197968241131520000

Offset

1,1

Comments

The number of free subgroups of index 12*n+{1,...,11} is 0, hence sequence is only for 12*n.

Links

Table of n, a(n) for n=1..16.

Wilfried Imrich, On the number of subgroups of given index in SL_2(Z), Archiv der Mathematik, vol. 31, 1978, pp. 224-231.

Formula

a(n) = 12*n*a(n-1) + Sum_{k = 1 .. n-2} a(k)*a(n-1-k) (Theorem 2 from Imrich).

Maple

a := proc(n) option remember: local i: if n = 1 then 20:
else 12*n*a(n-1)+add(a(k)*a(n-1-k), k = 1 .. n-2): fi: end:
seq(a(n), n = 1 .. 16);

Crossrefs

Sequence in context: A268884 A324069 A065412 * A159753 A252975 A000827

Adjacent sequences: A394647 A394648 A394649 * A394651 A394652 A394653

Keyword

nonn

Author

Lorenzo Sauras Altuzarra, Apr 24 2026

Status

approved